Positive solutions to a system of adjointable operator equations over Hilbert C∗-modules

We present necessary and sufficient conditions for the existence of a positive solution to the system of adjointable operator equations A1X=C1,XB2=C2,A3XB3=C3 over Hilbert C∗-modules. We also derive a representation for a general positive solution to this system when the solvability conditions are satisfied. The results of this paper extend some known results in the literature.